Question

Two twins, Mileena and Kitana, both wish to have the same amount of money save for retirement at age 65. Mileena saves $300 a month at an interest rate of 6% compounded monthly starting at age 25. If Kitana doesn't start saving until age 35, what must her monthly payments be (at the same interest rate) to have the same amount of money as Kitana at age 65

Answer 1

6% compounded monthly becomes 6/12 = 0.50% per month effectively.

Due to compound interest, Future value= Present value*(1+interest rate)^years

Excel's function =fv can be used to calculate future value.

=fv(rate,nper,pmt,pv)

Substitute rate as 0.5%, nper is number of periods = 12*(65-25) = 480 monthly  periods, pmt is the monthly payments which is 300, present value, pv is 0.

=fv(0.005,480,300,0)

=$597,447.22

Ignore the negative sign of excel as it shows monthly out flows of 300 needs to be done to receive an cash inflow of $597,447.22.

Now, to save the same money in (65-35) = 30 years, she would require as following.

=pmt function of Excel can be used

Number of periods = 12*(65-35) = 360

=pmt(rate,nper,pv,fv) . Pv is zero and fv is future value which is $597,447.22

=pmt(0.005,360,0,597,447.22)

=$594.76

Thus,$ 594.76 needs to be her monthly payments.